In this work we analyze a diffusion flame established in a low-permeability medium. A low-strained impinging jet of oxidant against a pool of low-volatility liquid fuel is the considered geometry. Owing to the differences on the transport properties of gas, liquid and solid, the problem presents physical processes occurring in different length scales. Hence, we perform an asymptotic analysis in order to obtain the profiles of temperature and species concentration in each length scale. As a result of the low-permeability feature of the medium, the velocity field is determined mainly by the gradient pressure (Darcy equation). The viscous effects become confined into small regions near the stagnation-point and the liquid-fuel interface. The effects of porosity, fuel Lewis number, strain-rate and liquid-fuel volatility on the flame temperature, flame position and vaporization rate are discussed. It is shown that the low-permeability medium is necessary in order to sustain the vaporization process of the low-volatility liquid fuel, as it enhances the heat transfer to the fuel reservoir. This model is valid for high rates of interphase heat exchange and low rates of strain. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.